If the cost price of 15 articles is equal to the selling price... | Mathematics MCQ | Examoogle

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If the cost price of 15 articles is equal to the selling price of 12 articles, what is the profit percentage?

$20\%$

$25\%$

$30\%$

$35\%$

Correct Answer

📐 MA • Math Ratio MethodMathematicsMathematics

Option B

$25\%$

Quick Summary:

Assume the total investment equals the LCM of 15 and 12 ( $60). \text{Then} CP of 1 article =$ 4 and SP of 1 article = $5, directly yielding a 25% profit.

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📐MAMath SolutionRatio Method

📋 Given

Cost price of 15 articles is equal to the selling price of 12 articles

🔢 Formula Used

Profit %=SP−CPCP×100\text{Profit } \% = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100Profit %=CPSP−CP​×100

⚡ Exam Hall Shortcut / Speed Trick

Assume the total investment equals the LCM of 15 and 12 ( $60). \text{Then} CP of 1 article =$ 4 and SP of 1 article = $5, directly yielding a 25% profit.

⚠️ Common Student Trap / Pitfall

Students often find the difference between 15 and 12 and divide incorrectly by the selling price quantity instead of the cost price base.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Set Up Equation

Translate the given statement into a mathematical equality between cost price and selling price.

15×CP=12×SP15 \times \text{CP} = 12 \times \text{SP}15×CP=12×SP

Determine Price Ratio

Rearrange the equation to find the ratio of selling price to cost price: $\frac{\text{SP}}{\text{CP}} = \frac{15}{12}$ .

SPCP=54\frac{\text{SP}}{\text{CP}} = \frac{5}{4}CPSP​=45​

Calculate Profit Percentage

Substitute the proportional values $\text{CP} = 4$ and $\text{SP} = 5$ into the profit percentage formula.

Profit %=5−44×100=25%\text{Profit } \% = \frac{5 - 4}{4} \times 100 = 25\%Profit %=45−4​×100=25%

✅

B is correct because the calculated profit percentage is 25%.

Core Concepts Used

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Cost Price and Selling Price Equivalence Profit and Loss Ratios Percentage Calculations

💡 EXAM TIP

This ratio equivalence approach is also extremely useful for solving problems involving marked price, discounts, and partnership investments.

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